It doesn't mean that CFLs are causing the problem…but I'm just thinking it could be a noise as small as that that seems big to your boy. So listen for small noises, buzzes, hums.
At our house we have CFL recessed lighting (and it makes a lot more noise than just the simple small ones in our lamps). It is like a soft high pitched buzz...but when you have multiples on at the same time, the noise is louder. I will also say that the noise changes based on the ambient temperature...colder - more noise, warmer - less noise. My b's don't seem to be bothered by it because they act no different if the lights are off or on.
Does the anxiety start in the hallways...or does it really seem to start once outdoors? Is he anxious in your apartment itself? And when you say he is anxious, can you describe the behaviour.
Well it does explain how he is hesitant to go to the door when it's time to go outside (the door to the hallway). He will always pause for a second before coming to me to put his leash on. I always wait by the door when it's time to go out. Sometimes he has refused to go to the door. He will peak around the corner in my foyer and then run back to the living room. It's not a playful hesitation either. It's without a doubt some sort of anxiety. There are probably a dozen overhead CFL bulbs on my floor.
He is sometimes anxious in my unit. The behavior is probably best described as him acting distracted, very concerned, etc. He won't be playful and usually just looks around. It's not common for him to be anxious inside my unit when I'm not leaving. Outdoors when he is anxious, it's the same behavior. Distracted, concerned, hesitant, etc. Sometimes he will jump up and back on his back legs trying to get out of his leash but that is not common.
I should note that I have been using a DAP diffuser in my unit for the last couple months. That has without a doubt helped, but it's not 100%.